Enzyme catalysts in living cells often couple two reactions so that an overall…

CHEMISTRY · Multi-part · A Level · Chemistry · Thermodynamics · Thermodynamics

Problem

Enzyme catalysts in living cells often couple two reactions so that an overall process becomes thermodynamically feasible. Step 1 (anabolic):

\text{A}\,(aq) + \text{B}\,(aq) \rightarrow \text{AB}\,(aq)

Step 2 (catabolic):

\text{C}\,(aq) \rightarrow \text{D}\,(aq) + \text{E}\,(aq)

The table lists the absolute molar entropies at 310 K (approximate physiological temperature).

Species	$S^\circ$ (J mol $^{-1}$ K $^{-1}$ )
$\text{A}\,(aq)$	125
$\text{B}\,(aq)$	132
$\text{AB}\,(aq)$	210
$\text{C}\,(aq)$	98
$\text{D}\,(aq)$	115
$\text{E}\,(aq)$	120

(a) Calculate

\Delta S^\circ_{310}

for Step 1 and for Step 2 separately. (b) Determine the overall

\Delta S^\circ_{310}

for the coupled reaction

\text{A} + \text{B} + \text{C} \rightarrow \text{AB} + \text{D} + \text{E}

. (c) Explain, with explicit reference to your calculations, why coupling Step 1 and Step 2 can render the overall biochemical transformation more favorable than Step 1 alone. (d) Propose one additional variable (other than entropy) that cells must control to ensure the coupled process proceeds efficiently, and briefly justify your choice.

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